According to the Daily Star, which carries reports from Spain, Real Madrid plan to move Ronaldo from his wide position to a more central role.
Benzema, who has been heavily linked with Arsenal and Liverpool in recent transfer windows, would be the odd man out in that case as he currently leads the Real Madrid attack.
Wenger on Pires
A Madrid source said: "He's [Cristiano Ronaldo] tall, strong, good in the air, fires the ball in on either leg…He has everything needed to be a great centre forward."
Benzema endured a miserable goal drought towards the end of the last campaign, and he reportedly came close to leaving the Bernabeu over the summer with several newspapers linking him to the Premier League.
The £40m-rated French international was linked with Liverpool before the Reds splashed out for Mario Balotelli, but Brendan Rodgers still has cash to spend in January after the Luis Suarez windfall and he may look to sign another forward.
Injury to Giroud
Arsenal meanwhile, are struggling up front with Olivier Giroud out of action until December at the earliest. A colleague of Benzema's at international level, Giroud suffered the injury against Everton at Goodison Park.
They signed Danny Welbeck from Manchester United on deadline day, but the England international has never been the most prolific. With Giroud out, the Gunners have to rely on Alexis Sanchez, Welbeck and Yaya Sanogo.
Sanchez is a fantastic player, but is yet to prove he's cut out to play through the middle for Arsenal. He struggled in his two outings in the position, against Everton, when he was replaced at half time, and against Southampton in the Capital One Cup, when he switched with Lukas Podolski.